Manufacturing Method of Flow Passage Network and Flow Passage Network Using the Same

ABSTRACT

An exemplary embodiment of the present invention relates to a manufacturing method of a flow passage network and a flow passage network for minimizing energy loss occurring during fluid flow. 
     An exemplary embodiment of the present invention provides a manufacturing method of a flow passage network including a flow passage in which a mother vessel having a radius of α 0  and a first branch and a second branch bifurcated from the mother vessel and having radiuses of α 1  and α 2 , respectively, the method including: a first step of setting a diameter D 0  of the mother vessel to 1 and setting the bifurcation angle θ 1  of the first branch to a predetermined value; a second step of calculating a diameter D 1  of the first branch by substituting the diameter D 0  of the mother vessel and the bifurcation angle θ 1  of the first branch set in the first step into 
     
       
         
           
             
               
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     a third step of calculating a diameter D 2  of the second branch by substituting the diameter D 0  of the mother vessel and the diameter D 1  of the first branch calculated in the second step into D 0   3 =D 1   3 +D 2   3 ; a fourth step of calculating a bifurcation angle θ 2  of the second branch by substituting the diameter D 0  of the mother vessel and the diameter D 2  of the second branch calculated in the third step into 
     
       
         
           
             
               
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     and a fifth step of checking whether the diameters D 0 , D 1 , and D 2  and the bifurcation angles θ 1 , θ 2 , and θ 1+2  have been calculated to have correct values by using 
     
       
         
           
             
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CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2009-0109301 filed in the Korean IntellectualProperty Office on Nov. 12, 2009, the entire contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

(a) Field of the Invention

The present invention relates to a manufacturing method of a flowpassage network and a flow passage network using the same, and moreparticularly, to a manufacturing method of a flow passage network and aflow passage network for minimizing energy loss occurring during fluidflow.

(b) Description of the Related Art

Fluid flow systems have been developed throughout the history of mankindover a long period of time. For example, there are agriculturalirrigation canals, urban water and sewage passages, transport passagesystems of industrial estates, etc. Further, small-scale bio-chips andblood circulation systems of human bodies can also be complex forms offlow passage networks.

Existing flow passages for transporting fluids have been manufacturedwhile emphasizing a proper function of “fluid transport”, and duringmanufacturing thereof, factors such as materials, spatial limits,processing techniques, and transport distances rather than geometricfactors for network organization or branching of flow passages have beenconsidered as important elements.

Particularly, even given that manufacturing microchannel networkscorresponding to flow passages of various bio-chips, DNA chips,micro-mixers, and μ-TAS (total analysis systems) having been spotlightedrecently, optimization based on a viewpoint of a geometric factor ortransport energy has been ignored. In this case, much flow loss occursdue to inefficiency of fluid transport.

Further, such flow passages cause an abnormal flow phenomenon such asflow separation and secondary flow due to inappropriate geometricfactors, thereby making smooth flow difficult and increasing flow loss.

Most of all, in view of an entire flow passage system, flow loss causesa great deal of energy loss. Therefore, a geometrically manufacturingmethod for improving an inefficient flow passage system is necessary.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the invention andtherefore it may contain information that does not form the prior artthat is already known in this country to a person of ordinary skill inthe art.

SUMMARY OF THE INVENTION

The present invention has been made in an effort to provide amanufacturing method of a flow passage network and a flow passagenetwork using the same having advantages of minimizing energy lossoccurring during flow.

An exemplary embodiment of the present invention provides amanufacturing method of a flow passage network including a flow passagein which a mother vessel having a radius of α₀ and a first branch and asecond branch bifurcated from the mother vessel and having radiuses ofα₁ and α₂, respectively, the method including: a first step of setting adiameter D₀ of the mother vessel to 1 and setting a bifurcation angle θ₁of the first branch to a predetermined value; a second step ofcalculating a diameter D₁ of the first branch by substituting thediameter D₀ of the mother vessel and a bifurcation angle θ₁ of the firstbranch set in the first step into

${{\cos \; \theta_{1}} = \frac{a_{0}^{4} + a_{1}^{4} - \left( {a_{0}^{3} - a_{1}^{3}} \right)^{4/3}}{2a_{0}^{2}a_{1}^{2}}};$

a third step of calculating a diameter D₂ of the second branch bysubstituting the diameter D₀ of the mother vessel and the diameter D₁ ofthe first branch calculated in the second step into D₀ ³=D₁ ³+D₂ ³; afourth step of calculating a bifurcation angle θ₂ of the second branchby substituting the diameter D₀ of the mother vessel and the diameter D₂of the second branch calculated in the third step into

${{\cos \; \theta_{2}} = \frac{a_{0}^{4} - \left( {a_{0}^{3} - a_{2}^{3}} \right)^{4/3} + a_{2}^{4}}{2a_{0}^{2}a_{2}^{2}}};$

and a fifth step of checking whether the diameters D₀, D₁, and D₂ andthe bifurcation angles θ₁, θ₂, and θ₁₊₂ have been calculated to havecorrect values by using

${\cos \left( \theta_{1 + 2} \right)} = {\frac{\left( {a_{1}^{3} + a_{2}^{3}} \right)^{4/3} - a_{1}^{4} - a_{2}^{4}}{2a_{1}^{2}a_{2}^{2}}.}$

The manufacturing method of a flow passage network according to theexemplary embodiment of the present invention may further include asixth step of determining whether any one of the first branch and thesecond branch is bifurcated, returning to the first step in order todetermine geometric factors of the next branches when any one of thefirst branch and the second branch is branched, and finishing when anyone of the first branch and the second branch is not bifurcated.

The manufacturing method of a flow passage network according to theexemplary embodiment of the present invention may further include aseventh step of calculating a global flow resistance P_(total) of theflow passage network by adding a manufacture condition regarding thediameters and lengths of the branches by using

$P_{total} = {{\sum\limits_{i = 0}^{n}{\Delta \; p_{i}}} = {\frac{128\; v}{\pi}\overset{.}{m}{\sum\limits_{i = 0}^{n}\frac{L_{i}}{D_{i}^{4}}}}}$

after the sixth step.

Another exemplary embodiment of the present invention provides a flowpassage network using the manufacturing method of a flow passagenetwork.

The branches may be symmetric bifurcations having the same diameter.

The branches may have a bifurcation angle range of 37.5°±2° with respectto the mother vessel, respectively.

The diameters and lengths of the mother vessel and the branches maydecrease at a ratio of 2^(−1/3).

As described above, according to the exemplary embodiments of thepresent invention, there are effects in which flow loss is reducedduring fluid transport and the energy efficiency of flow passagesincreases by optimizing geometric factors of flow passages on the basisof biomimetic techniques and theoretical formulae of fluid mechanics.Further, it is effective in manufacturing microfluidics in which laminarflow with a low Reynolds number is dominant.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a flowchart of a manufacturing method of a flow passagenetwork according to an exemplary embodiment of the present invention.

FIG. 2 shows a schematic diagram of a branched passage applied to a flowpassage network manufactured according to an exemplary embodiment of thepresent invention.

FIG. 3 shows a schematic diagram of fluid flow inside a circular tube.

FIG. 4 shows a schematic diagram of a flow passage network composed of acombination of branched passages.

FIG. 5 shows a schematic diagram of a flow passage network using themanufacturing method of FIG. 1.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention will be described more fully hereinafter withreference to the accompanying drawings, in which exemplary embodimentsof the invention are shown. As those skilled in the art would realize,the described embodiments may be modified in various different ways, allwithout departing from the spirit or scope of the present invention. Thedrawings and description are to be regarded as illustrative in natureand not restrictive. Like reference numerals designate like elementsthroughout the specification.

FIG. 1 shows a flowchart of a manufacturing method of a flow passagenetwork (hereinafter referred to as “a manufacturing method” forconvenience) according to an exemplary embodiment of the presentinvention, and FIG. 2 shows a schematic diagram of bifurcated branchesapplied to a flow passage network manufactured according to an exemplaryembodiment of the present invention.

Referring to FIGS. 1 and 2, an exemplary embodiment shows a method ofoptimizing geometric factors upon which a first branch 21 and a secondbranch 22 are bifurcated from a mother vessel 10, and exemplarily showsthe individual lengths L₀, L₁, and L₂, diameters D₀, D₁, and D₂, andbifurcation angles θ₁, θ₂, and θ₁₊₂ of the mother vessel 10, the firstbranch 21, and the second branch 22, in order to minimize flow lossoccurring in a flow passage 2.

As shown in FIG. 2, the flow passage 2 may be configured in a singlebifurcation form in which the first branch 21 and the second branch 22are bifurcated from the mother vessel 10, or may be configured in formsof flow passage networks 4 and 6 (see FIGS. 4 and 5) by combining singlebifurcations if necessary. Therefore, the manufacturing method accordingto the present exemplary embodiment is not limited to determininggeometric factors in the flow passage 2 of a single bifurcation, butalso includes determining geometric factors in the flow passage networks4 and 6.

Referring to FIG. 2, the length L₀ is set between one end of the mothervessel 10 and a bifurcated point B, the length L₁ is set between thebifurcated point B and an end of the first branch 21, and the length L₂is set between the bifurcated point B and an end of the second branch22. The diameters D₀, D₁, and D₂ are set in the mother vessel 10, thefirst branch 21, and the second branch 22, respectively. The bifurcationangle θ₁ is set between an extended center line of the mother vessel 10and the first branch 21, the bifurcation angle θ₂ is set between anextended center line of the mother vessel 10 and the second branch 22,and the bifurcation angle θ₁₊₂ is set between the first branch 21 andthe second branch 22.

The manufacturing method according to the present exemplary embodimenthas been developed on the basis of observation of microcirculationsystems of human bodies and hydrodynamic theoretical formulae.

FIG. 3 shows a schematic diagram of fluid flow inside a circular tube.Referring to FIG. 3, when flow in a circular tube 8 has a laminar flowcharacteristic, the Hagen-Poiseuille flow, a pressure drop Δp, andwall-face shearing stress τ_(w) are the same as in Equation 1, and aflow rate Q (=inflow rate Q_(in)=outflow rate Q_(out)) is the same as inEquation 2.

$\begin{matrix}{{\Delta \; p} = \frac{4L\; \tau_{w}}{D}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack \\{Q = {\frac{\pi \; D^{4}\Delta \; p}{128\mspace{11mu} \mu \; L}\mspace{25mu} \left( {{{or}\mspace{14mu} \Delta \; p} = {\frac{128\mspace{11mu} \mu \; L}{\pi \; D^{4}}Q}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

Here, D is the diameter of the circular tube 8, L is the length of thecircular tube 8, and μ is a viscosity coefficient of a fluid.

Meanwhile, according to Murray's law derived by a minimum workprinciple, in order to minimize flow energy loss of a fluid flowing fromthe mother vessel 10 to the first branch 21 and the second branch 22(see FIG. 2), the relationship as in Equation 3 should be established.

D ₀ ³ =D ₁ ³ +D ₂ ³  [Equation 3]

Further, in order to minimize the flow energy loss, the relationships asin Equations 4 to 6 between optimal bifurcation angles θ₁, θ₂, and θ₁₊₂and the diameters D₀, D₁, and D₂ of the mother vessel 10 and the firstand second branches 21 and 22 are established. Since α is the radius ofthe passage, the relationship of D=2α is established. That is, therelationships of α₀=D₀/2, α₁=D₁/2, and α₂=D₂/2 are established.

$\begin{matrix}{{\cos \; \theta_{1}} = \frac{a_{0}^{4} + a_{1}^{4} - \left( {a_{0}^{3} - a_{1}^{3}} \right)^{4/3}}{2a_{0}^{2}a_{1}^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack \\{{\cos \; \theta_{2}} = \frac{a_{0}^{4} - \left( {a_{0}^{3} - a_{2}^{3}} \right)^{4/3} + a_{2}^{4}}{2a_{0}^{2}a_{2}^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \\{{\cos \left( \theta_{1 + 2} \right)} = \frac{\left( {a_{1}^{3} + a_{2}^{3}} \right)^{4/3} - a_{1}^{4} - a_{2}^{4}}{2a_{1}^{2}a_{2}^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

It is possible to optimize the flow passage 2 composed of the singlebifurcation of the mother vessel 10 and the first and second branches 21and 22 through the relational equations between the geometric factors,that is, Equations 3 to 6, and it is possible to optimize the entireflow passage networks 4 and 6 composed of a combination of suchoptimized signal bifurcations.

In general, Murray's law relates to a minimizing energy required forfluid flow. It is known that the mother vessel 10 and the first andsecond branches 21 and 22 manufactured on the basis of Murray's lawminimize flow disturbances at the bifurcated point B (see FIG. 2).Particularly, an exponent 3 seen in Murray's law has a low losscoefficient with respect to diameter ratio of almost all branches.

The manufacturing method of the flow passage 2 according to an exemplaryembodiment may be implemented as a manufacturing process shown inFIG. 1. The manufacturing method of an exemplary embodiment includes afirst step ST10, a second step ST20, a third step ST30, a fourth stepST40, a fifth step ST50, and a sixth step ST60.

The first step ST10 sets the diameter D₀ of the mother vessel 10 to 1,and sets the bifurcation angel θ₁ of the first branch 21 to apredetermined value that is a known design specification value.

The second step ST20 calculates the diameter D₁ of the first branch 21by substituting the diameter D₀ of the mother vessel 10 and thebifurcation angle θ₁ of the first branch 21 set in the first step ST10into Equation 4.

The third step ST30 calculates the diameter D₂ of the second branch 22by substituting the diameter D₀ of the mother vessel 10 and the diameterD₁ of the first branch 21 calculated in the second step ST20 intoEquation 3.

The fourth step ST40 calculates the bifurcation angle θ₂ of the secondbranch 22 by substituting the diameter D₀ of the mother vessel 10 andthe diameter D₂ of the second branch 22 calculated in the third stepST30 into Equation 5.

The fifth step ST50 checks whether all the geometric factors D₀, D₁, D₂,θ₁, θ₂, and θ₁₊₂ having been calculated in the first, second, third, andfourth steps ST10, ST20, ST30, and ST40 have correct values by usingEquation 6.

The sixth step ST60 determines whether a next bifurcated stage is in thefirst or second branch 21 or 22. When the first or second branch 21 or22 is bifurcated, the process returns to the first step ST10 tocalculate geometric factors of the next branches. When the first andsecond branches 21 and 22 are not bifurcated, the process finishes. Whenthe first or second branch 21 or 22 is bifurcated, the first or secondbranch 21 or 22 becomes a mother vessel and the next branches becomefirst and second branches.

It is possible to manufacture the mother vessel 10 and the first andsecond branches 21 and 22 with desired design specification valuesthrough the first to sixth steps ST10 to ST60, and it is possible tooptimize the entire flow passage networks 4 and 6 composed of acombination of bifurcated branches by performing calculations withrespect to the next branches (not shown) bifurcated from the first orsecond branch 21 or 22 by repeating the same process.

The manufacturing method according to the exemplary embodimentexemplifies a method of calculating the other geometric factors D₁, D₂,D₂, and θ₁₊₂ from the diameter D₀ of the mother vessel 10 and thebifurcation angle θ₁ of the first branch 21. Further, even though notshown, it is possible to calculate the other geometric factors D₂, θ₁,θ₂, and θ₁₊₂ from the diameter D₀ of the mother vessel 10 and thediameter D₁ of the first branch 21, and it is possible to calculate theother geometric factors D₁, θ₁, θ₂, and θ₁₊₂ from the diameter D₀ of themother vessel 10 and the diameter D₂ of the second branch 22.

In order to verify Equations 3 to 6 and obtain information of thegeometric factors actually used during manufacturing of the flow passage2, the results in Table 1 (measured values of geometric factors ofcirculation systems) were obtained by performing measurement withrespect to circulation systems of living bodies.

TABLE 1 Bifurcation Factor Measured Value Cross-sectional area ratio γ(=(D₁ ² + D₂ ²)/D₀ ²) 1.209 Ratio of Murray's law α (=D₀ ³/(D₁ ³ + D₂³)) 1.053 D₁/D₀ 0.786 D₂/D₁ 1.001 D₂/D₀ 0.743 Bifurcation angle of FirstBranch θ₁, (°) 37.434 Bifurcation angle of Second Branch θ₂, (°) 39.726Bifurcation angle θ₁₊₂, (°) 77.161

In Table 1, the ratio D₂/D₁ of the diameters D₁ and D₂ of the first andsecond branches 21 and 22 is 1.001, which means that almost all branchesexisting in a circulation system of a living body have the symmetricbifurcation (D₁=D₂) pattern.

If a calculation is performed by substituting D₁=D₂ into Equations 3 to6 on the basis of the measured results, it can be seen that the measuredvalues shown in Table 1 are very similar to the theoretical values(D₁/D₀=D₂/D₀=2^(−1/3)≈0.794, γ=2^(1/3)≈1.260, θ₁=θ₂=37.5° of thegeometric factors of the symmetric branch system.

The manufacturing method of the first to sixth steps ST10 to ST60 iseffective as manufacturing guidelines of each of the first and secondbranches 21 and 22. However, in order to manufacture the configurationof the entire flow passage network 4 or 6, manufacture conditions of thediameters D₁ and D₂ and lengths L₁ and L₂ of the first and secondbranches 21 and 22 are additionally required.

Therefore, the manufacturing method of an exemplary embodiment mayfurther include a seventh step ST70. The seventh step ST70 optimizes theglobal flow resistance of the flow passage network 4 that issequentially bifurcated.

FIG. 4 shows a schematic diagram of a flow passage network composed of acombination of bifurcated branches. Referring to FIG. 4, additionalmanufacturing conditions of the flow passage network 4 are derivedthrough optimization of the global flow resistance of the flow passagenetwork 4 that is sequentially bifurcated as shown in FIG. 4.

The global flow resistance P_(total) of the flow passage network 4 shownin FIG. 4 is the same as in Equation 7.

$\begin{matrix}{P_{total} = {{\sum\limits_{i = 0}^{n}{\Delta \; p_{i}}} = {\frac{128\; v}{\pi}\overset{.}{m}{\sum\limits_{i = 0}^{n}\frac{L_{i}}{D_{i}^{4}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Here, v and {dot over (m)} represent the kinematic viscosity coefficientand a mass flow rate, respectively, and i represents a bifurcationgeneration number.

A resistance factor which is an important geometric factor having agreat effect on the global flow resistance P_(total) can be consideredas L/D⁴ represented by a ratio of a length L and a diameter D. Amanufacturing condition of the length L and the diameter D which aregeometric factors constituting the resistance factor is obtained asfollows. First, in a case of symmetric bifurcation (D₁=D₂), Murray's lawof Equation 3 is the same as in Equation 8.

D_(i) ³=2D_(i-1) ³ (or D_(i-1) ³=2D_(i) ³)  [Equation 8]

A volume V_(i) of a branch in each bifurcation generation of FIG. 4 isexpressed as Equation 9.

${V_{i} = {{\frac{2^{i}\pi \; D_{i}^{2}}{4}L_{i}\mspace{25mu} i} = 0}},1,\ldots \mspace{14mu},n$

If a condition in which volumes of branches in each bifurcationgeneration i are the same (V_(i) is constant) is applied to Equation 9,the manufacturing condition of the diameter D and length L of a branchis determined.

$V_{i} = {\left. {\frac{2^{i}\pi \; D_{i}^{2}}{4}L_{i}}\Rightarrow{2^{i}D_{i}^{2}L_{i}} \right. = c}$$\frac{2^{i + 1}D_{i + 1}^{2}L_{i + 1}}{2^{i}D_{i}^{2}L_{i}} = 1$

Here, since

$\frac{2^{i + 1}}{2^{i}} = {{2\mspace{14mu} {and}\mspace{14mu} \left( \frac{D_{i + 1}}{D_{i}} \right)^{2}} = 2^{- \frac{2}{3}}}$

(see Equation 8) are satisfied,

$\left( \frac{L_{i + 1}}{L_{i}} \right) = 2^{- \frac{1}{3}}$

is satisfied. That is, a reduction ratio of the diameter D and thelength L is the same as in Equation 10.

$\begin{matrix}{\left( \frac{D_{i + 1}}{D_{i}} \right) = {2^{- \frac{1}{3}} = {{0.7937\mspace{14mu} {or}\mspace{14mu} \left( \frac{L_{i + 1}}{L_{i}} \right)} = {2^{- \frac{1}{3}} = 0.7937}}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

As the generation number increases in the flow passage network 4, it ispossible to minimize loss caused by the flow resistance, if the length Land the diameter D are reduced at a ratio of 2^(−1/3), that is, by about20.63%.

FIG. 5 shows a schematic diagram illustrating a flow passage networkusing the manufacturing method of FIG. 1. Referring to FIG. 5, a flowpassage network 6 manufactured by applying the manufacturing method ofan exemplary embodiment is illustrated.

Since the flow passage network 6 that is optimally manufacturedoptimizes individual branches and the entire flow passage 6 throughEquations 1 to 10, it is possible to minimize flow loss.

Further, even though the description has been made in an exemplaryembodiment by exemplifying the flow passage network in which the mothervessel and the branches are formed to have a circular cross-section, theexemplary embodiment can be applied in the same way to a flow passagenetwork configured to have a rectangular cross-section.

While this invention has been described in connection with what ispresently considered to be practical exemplary embodiments, it is to beunderstood that the invention is not limited to the disclosedembodiments, but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

DESCRIPTION OF SYMBOLS

-   -   2: Flow passage 4, 6: Flow passage network    -   8: Circular tube 10: mother vessel    -   21, 22: first and second branch B: Branched point    -   D₀, D₁, D₂: Diameter L₀, L₁, L₂: Length    -   θ₁, θ₂, θ₁₊₂: Bifurcation angle

1. A manufacturing method of a flow passage network including a flowpassage in which a mother vessel having a radius of α₀ and a firstbranch and a second branch bifurcated form the mother vessel and havingradiuses of α₁ and α₂, respectively, the method comprising: a first stepof setting a diameter D₀ of the mother vessel to 1 and setting abifurcation angle θ₁ of the first branch to a predetermined value; asecond step of calculating a diameter D₁ of the first branch bysubstituting the diameter D₀ of the mother vessel and a bifurcationangle θ₁ of the first branch set in the first step into${{\cos \; \theta_{1}} = \frac{a_{0}^{4} + a_{1}^{4} - \left( {a_{0}^{3} - a_{1}^{3}} \right)^{4/3}}{2a_{0}^{2}a_{1}^{2}}};$a third step of calculating a diameter D₂ of the second branch bysubstituting the diameter D₀ of the mother vessel and the diameter D₁ ofthe first branch calculated in the second step into D₀ ³=D₁ ³+D₂ ³; afourth step of calculating a bifurcation angle θ₂ of the second branchby substituting the diameter D₀ of the mother vessel and the diameter D₂of the second branch calculated in the third step into${{\cos \; \theta_{2}} = \frac{a_{0}^{4} - \left( {a_{0}^{3} - a_{2}^{3}} \right)^{4/3} + a_{2}^{4}}{2a_{0}^{2}a_{2}^{2}}};$ and a fifth step of checking whether the diameters D₀, D₁, and D₂ andthe bifurcation angles θ₁, θ₂, and θ₁₊₂ have been calculated to havecorrect values by using${\cos \left( \theta_{1 + 2} \right)} = {\frac{\left( {a_{1}^{3} + a_{2}^{3}} \right)^{4/3} - a_{1}^{4} - a_{2}^{4}}{2a_{1}^{2}a_{2}^{2}}.}$2. The method of claim 1, further comprising a sixth step of determiningwhether any one of the first branch and the second branch is bifurcated,returning to the first step in order to determine geometric factors ofthe next branches when any one of the first branch and the second branchis branched, and finishing when both the first branch and the secondbranch are not bifurcated.
 3. The method of claim 2, further comprisingafter the sixth step, a seventh step of calculating a global flowresistance P_(total) of the flow passage network by adding a manufacturecondition regarding the diameters and lengths of the branches by using$P_{total} = {{\sum\limits_{i = 0}^{n}{\Delta \; p_{i}}} = {\frac{128\; v}{\pi}\overset{.}{m}{\sum\limits_{i = 0}^{n}{\frac{L_{i}}{D_{i}^{4}}.}}}}$4. A flow passage network using the manufacturing method of a flowpassage network of claim
 1. 5. The flow passage network of claim 4,wherein the branches are symmetric bifurcations having the samediameter.
 6. The flow passage network of claim 5, wherein the brancheshave a bifurcation angle range of 37.5°±2° with respect to the mothervessel, respectively.
 7. The flow passage network of claim 5, whereinthe diameters and lengths of the mother vessel and the branches decreaseat a ratio of 2^(−1/3).
 8. A flow passage network using themanufacturing method of a flow passage network of claim
 2. 9. The flowpassage network of claim 8, wherein the branches are symmetricbifurcations having the same diameter.
 10. The flow passage network ofclaim 9, wherein the branches have a bifurcation angle range of 37.5°±2°with respect to the mother vessel, respectively.
 11. The flow passagenetwork of claim 9, wherein the diameters and lengths of the mothervessel and the branches decrease at a ratio of 2^(−1/3).
 12. A flowpassage network using the manufacturing method of a flow passage networkof claim
 3. 13. The flow passage network of claim 12, wherein thebranches are symmetric bifurcations having the same diameter.
 14. Theflow passage network of claim 13, wherein the branches have abifurcation angle range of 37.5°±2° with respect to the mother vessel,respectively.
 15. The flow passage network of claim 13, wherein thediameters and lengths of the mother vessel and the branches decrease ata ratio of 2^(−1/3).